Mathematics

Problem

Consider

f:\mathbb R\to\mathbb R

given by

f(x)=\sqrt{2x+1}

(with its usual domain) and

g:\mathbb R\setminus\{3\}\to\mathbb R

given by

g(t)=\dfrac{1}{t-3}

. Which of the following is the largest possible domain of

f

so that

g\circ f

is well-defined? a)

(4,\infty)

\bigl[-\tfrac12,\infty\bigr)

\bigl[-\tfrac12,\infty\bigr)\setminus\{4\}

\bigl[-\tfrac12,4\bigr)